Then thanks friendo. It's just not everyday you meet someone with that high level of empathy. I'm not sure if I ever insulted you. If I did, I apologize.

So, the issue I have is that you refuse to give me your definition of an infinite sum. I think you equate it with Riemman zeta function, but what then is your definition of the Riemman zeta function?

In my book, it's defined as analytic extension of some infinite sum. So, if that sum is defined by Riemman zeta function, that's a cyclic definition.

With my definitions, I have proven to you that the statement "the sum of all natural numbers is -1/12" is contradictory. Until you give me your definitions, we can't establish a formal mathematical discussion.

All we can do is make pleas to authority and say things like

Column A: Riemman (though I think he only created the function), Ramanujan and Euler

Column B: Every current mathematician with a masters degree.